~ 2.4 ~

The table shows the amount of red paint and blue paint needed to make a certain shade of purple paint, called Venusian Sunset.

Note that “parts” can be any unit for volume. If we mix 3 cups of red with 12 cups of blue, you will get the same shade as if we mix 3 teaspoons of red with 12 teaspoons of blue

The last row in the table says that if we know the amount of red paint needed, r, we can always multiply it by 4 to find the amount of blue paint needed, b, to mix with it to make Venusian Sunset. We can say this more succinctly with the equation b=4r. So the amount of blue paint is proportional to the amount of red paint and the constant of proportionality is 4.

We can also look at this relationship the other way around.

If we know the amount of blue paint needed, b, we can always multiply it by ¼ to find the amount of red paint needed, r, to mix with it to make Venusian Sunset. So r = ¼ b. The amount of blue paint is proportional to the amount of red paint and the constant of proportionality ¼.

In general, when y is proportional to x, we can always multiply x by the same number k—the constant of proportionality—to get y. We can write this much more succinctly with the equation y=kx.

Dry Rice

A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.

1. How many people will 1 cup of rice serve?
2. How many people will 3 cups of rice serve? 12 cups? 43 cups?
3. How many people will x cups of rice serve? Hint: Write an equation.

Spring Rolls

A recipe says that 6 spring rolls will serve 3 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.

1. How many people will 1 spring roll serve?
2. How many people will 10 spring rolls serve? 16 spring rolls? 25 spring rolls?
3. How many people will n spring rolls serve? Hint: Write an equation.
4. How was completing this table different from the previous table? How was it the same?